Q 12-12-014NEETJEE MainMedium
The speed of the electron in the first Bohr orbit of hydrogen is about $2.2 \times 10^6$ m/s. Its speed in the third orbit of doubly ionised lithium ($Z = 3$) is
Answer: (C) $2.2 \times 10^6$ m/s
Concept. In the Bohr model $v_n = v_1\dfrac{Z}{n}$, where $v_1 = 2.2 \times 10^6$ m/s is hydrogen's first-orbit speed.
Step 1. Substitute. For Li$^{2+}$, $Z = 3$, $n = 3$:
$$v = 2.2 \times 10^6 \times \frac{3}{3} = 2.2 \times 10^6\ \text{m/s}$$
Answer. $2.2 \times 10^6$ m/s (Option C).
Solution by Sreeraj P, M.Sc Physics